An optical information processing apparatus using the holography is a kind of page-oriented memories and uses a parallel signal processing as an input/output method. Accordingly, a holographic optical information processing apparatus can perform data processing faster than a CD (Compact Disk) or DVD (Digital Versatile Disk) which records or reproduces data by a bit.
An optical information processing apparatus using the holography performs recording operation by projecting an information beam, which contains an image information of data to record, and a reference beam, which is to be interfered with the information beam, to an optical information recording medium (ex, optical data storage). In the other hand, for reproducing, the reference beam is projected to the optical information recording medium, a reproduced beam, which is diffracted from the recording medium, is detected by an optical information detector such as a CMOS (Complementary Metal-Oxide Semiconductor) or CCD (Charge Coupled Device), and original data is reproduced by signal processing and decoding.
However, due to variations of channel characteristic such as contraction of the optical information recording medium, the detected data page may have errors when an image of data page is detected by the optical information detector. For example, a pixel of the data page (hereinafter, called as ‘a data pixel’) and a pixel of the optical information detector (hereinafter called as ‘a detecting pixel’) may not match with each other due to a mis??alignment. These errors may cause a fairly high bit error rate (BER).
To decrease BER, an error correction code (ECC) is introduced. Among ECCs, there is a low density parity check (LDPC) code whose performance close to the Shannon's theoretical limitation of the channel capacity. The LDPC code is a linear block code where most elements of the parity check matrix are symbol “0.”
A parity check code has a block which contains information symbols and parity check symbols which is a modulo sum of specific information symbols so that it constitutes a code word.
The relation between the check symbols and the information symbols can be represented by a parity check matrix “H”. The parity check matrix H can be represented by a set of linear homogeneous equations. That is, LDPC code is one of parity check codes and it has a parity check matrix of which most elements are symbol “0” and the remains have randomly scattered weights.
Encoding process of the LDPC code with the parity check matrix H is described as follows. When the parity check matrix H is achieved, a generator matrix G, which corresponds to the parity check matrix H, is generated by using the relation GHT=0. A code word C, which corresponds to the information symbol block X, can be achieved from the relation C=XG. If numbers W and Wx (N/M) with respect to the matrix H (H=N×M) are constant, where the number W is the number of is per each column and the number Wx (N/M) is the number of 1s per each raw, it is called as a regular LDPC code.
If the number of 1s per each column is not constant and the number of is per each raw is not exactly equal to Wax (N/M), it is called as an irregular LDPC code. It is generally known that an irregular LDPC code has better error correction capacity but it is harder to embody by hardware than a regular LDPC code.
Decoding of the LDPC code means the operation to detect the most probably approximate code word, which satisfies the relation where the product with the matrix H is equal to 0, from received signal vectors.
The sum-product algorithm among decoding methods of the LDPC code performs a soft decision iterative decoding using probability values. According to the sum-product algorithm, decoding is performed iteratively, while massages of probability are transmitted among nodes in the code word graph, until the code word, which satisfies the criteria of the maximum likelihood, is achieved.
There is another decoding method of LDPC code, so called LLR algorithm, which use a log-likelihood ratio (LLR). With respect to the LLR algorithm, Korean registered patent No. 10-0538281 can be referred.
The LLR algorithm is described in brief as follows. A LDPC decoder calculates initial LLR after calculating probabilities for each case when the data pixel is symbol “0” or “1”.